Abstract

A correspondence principle for free vibrations in the classical linearized theory of viscoelasticity is established. It is shown that, for motions which are either irrotational or solenoidal, there is always an associated elastic problem with the following properties: (a) Every mode shape for the viscoelastic problem is also a mode shape for the elastic problem; and (b) the viscoelastic frequencies can, in principle, be calculated from a knowledge of the elastic spectrum and the relevant relaxation function. It is further shown that, in general, for motions which are neither irrotational nor solenoidal, this correspondence exists only for the restricted class of viscoelastic materials for which the behavior depends essentially upon one relaxation function. The paper concludes with the observation that the correspondence also exists for those approximate theories in which there appears only one relaxation function.

Return to: A Correspondence Principle for Free Vibrations of a Viscoelastic Solid

Copyright in the material you requested is held by the American Society of Mechanical Engineers (unless otherwise noted). This email ability is provided as a courtesy, and by using it you agree that you are requesting the material solely for personal, non-commercial use, and that it is subject to the American Society of Mechanical Engineers' Terms of Use. The information provided in order to email this topic will not be used to send unsolicited email, nor will it be furnished to third parties. Please refer to the American Society of Mechanical Engineers' Privacy Policy for further information.

Shibboleth is an access management service that provides single sign-on protected resources.
It replaces the multiple user names and passwords necessary to access subscription-based content with a single user name and password that can be entered once per session.
It operates independently of a user's location or IP address.
If your institution uses Shibboleth authentication, please contact your site administrator to receive your user name and password.